[Mitgcm-support] Re: detatfreesurf == deltatracer

[mitgcm-support at dev.mitgcm.org]

Hi, 

For the NLFS and specially with real freah water input, 
its clear that for consistency, deltaT_freesurf needs to
be set to deltaT_tracer.
By the way, deltaT_freesurf is not the time step of 
barotropic mode but only the time step of the free 
surface equation d.eta/dt = -Div.U.
the equivalent time step of the barotropic mode is 
in fact the square root of deltaT_freesurf*deltaT_Mom

For Linear free surface,
my interpretation is that the implicit method
filters/damps the fast motions (here d.eta/dt) what 
cannot be (accurately) represented by the time step,
and conserve the slow motions that the time step 
allows to represent accurately.
The part of the free surface that matters for the tracer
is d.eta/dt (= w at the surface, but also a contribution to
w at each level that decreasing linearly to 0 at the bottom)
For the momentum, its mainly the surface pressure gradient.

When deltaT_tracer = 72 * deltaT_Mom: the solver filters/damps 
variations of eta that are fast relative to deltaT_freesurf; 
if deltaT_freesurf=deltaT_Mom, 
w_s = d.eta/deltaT_freesurf can still be too large for the tracer eq 
(w_s*deltaT_tracer) given the long tracer time step, even if it is 
small enough regarding the implicit method "criteria" (enough damping) 
because of the small time step deltaT_freesurf.
So I think that the safe way to use multiple time step is
to give the right (long) time step to the solver 
(deltaT_freesurf=deltaT_tracer), so that it will damp enough 
w_s according to this "long" time step.
And deltaT_Mom is still used for the
surface pressure gradient term, like it is now.

Alternatively, we could have defined a barotropic time step
and use this one every where in the solve_for_P part of the code, 
both for the surface pressure term and the divergence of the flow.
it could be set to the square root of deltaT_tracer*deltaT_Mom
with similar effects compared to deltaT_freesurf=deltaT_tracer. 
But I don't think its a good method because its not 
consistent with anay other parts of the model (Tracer, momentum,
real fresh water forcing ...).

For rigid lid case, I was thinking (?) that deltaT_freesurf
was not used. Is it right ?

Jean-Michel